The planes, which are currently in Melbourne and Sydney, Australia and in London, England, will be flown to Singapore where they will receive new engines.
The move comes less than a week after an engine on a Qantas A380 exploded shortly after takeoff, forcing Qantas to ground its fleet of A380s.
Singapore Airlines, however, does not know whether the oil stains found on its engines have any connection with the oil leaks found on the Qantas aircraft.
Aerospace experts say the most likely cause of an oil leak or stain is a tiny crack in the oil supply pipe that lubricates the engine's bearings. Oil leaks in an engine's turbine area can spark fires, which could then put excessive stress on the engine parts and lead to a breakdown.
The Australian Transport Safety Bureau is leading an international investigation of the Qantas incident.
The Associated Press contributed to this report.